# Variational Message Passing with Structured Inference Networks

arXiv: https://arxiv.org/abs/1803.05589 · HTML: https://mlsanity.com/paper/1803.05589/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Mar 2018.

## Built on by (most cited first, 17 of 17)

- [Graph-Guided Network for Irregularly Sampled Multivariate Time Series](https://mlsanity.com/paper/2110.05357/) (2021)
- [Revisiting Structured Variational Autoencoders](https://mlsanity.com/paper/2305.16543/) (2023)
- [Physics-enhanced Gaussian Process Variational Autoencoder](https://mlsanity.com/paper/2305.09006/) (2023)
- [Unbiased Learning of Deep Generative Models with Structured Discrete Representations](https://mlsanity.com/paper/2306.08230/) (2023)
- [Exploiting Inferential Structure in Neural Processes](https://mlsanity.com/paper/2306.15169/) (2023)
- [Variational excess risk bound for general state space models](https://mlsanity.com/paper/2312.09607/) (2023)
- [Tree-based variational inference for Poisson log-normal models](https://mlsanity.com/paper/2406.17361/) (2024)
- [Realising Active Inference in Variational Message Passing: the Outcome-blind Certainty Seeker](https://mlsanity.com/paper/2104.11798/) (2021)
- [Structured Recognition for Generative Models with Explaining Away](https://mlsanity.com/paper/2209.05212/) (2022)
- [Importance sampling for online variational learning](https://mlsanity.com/paper/2402.02859/) (2024)
- [Efficient Online Variational Estimation via Monte Carlo Sampling](https://mlsanity.com/paper/2602.06579/) (2026)
- [PAC-Bayesian Reconstruction Guarantees for Time Series Variational Autoencoders](https://mlsanity.com/paper/2609.05212/) (2026)
- [Meta-Learning with Variational Bayes](https://mlsanity.com/paper/2103.02265/) (2021)
- [Amortized backward variational inference in nonlinear state-space models](https://mlsanity.com/paper/2206.00319/) (2022)
- [Amortised Inference in Bayesian Neural Networks](https://mlsanity.com/paper/2309.03018/) (2023)
- [Stability Enhanced Gaussian Process Variational Autoencoders](https://mlsanity.com/paper/2604.09331/) (2026)
- [Information Geometry of Message Passing](https://mlsanity.com/paper/2608.15922/) (2026)

## Abstract (arXiv)

Recent efforts on combining deep models with probabilistic graphical models are promising in providing flexible models that are also easy to interpret. We propose a variational message-passing algorithm for variational inference in such models. We make three contributions. First, we propose structured inference networks that incorporate the structure of the graphical model in the inference network of variational auto-encoders (VAE). Second, we establish conditions under which such inference networks enable fast amortized inference similar to VAE. Finally, we derive a variational message passing algorithm to perform efficient natural-gradient inference while retaining the efficiency of the amortized inference. By simultaneously enabling structured, amortized, and natural-gradient inference for deep structured models, our method simplifies and generalizes existing methods.